Let a binary operation '*' be defined on I (set of integers) by : a * b = 2a + 2b for `a, b in I`. Prove that given operation is commutative but not associative.

Let a binary operation '*' be defined on Z by a * b = 2 a + 2b for all a, b in Z. Prove that the given operawtion is commutative but not associative.

Let a mapping '*' from R xx R to R be defined by a * b = 2 a + 2 b for all a , b in Z. Prove that the givne operation is commutative but not associative.

Let S be the set of all real numbers except 1 and 'o' be an operation on S defined by : aob = a+b - ab for all a,b in S. Prove that the given operation is : (I) commutative (II) associative.

Consider the operations '*' and o+ on the set R of all real numbers defined as a* b = |a-b| and a o+ b = a for all a, b in R. Prove that '*' is commutative but not associative.

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b = a-b, for a , b in Q. Find which of the binary operations are commutative and which are associative.

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b =a+ab, for a, b in Q.Find which of the binary operations are commutative and which are associative.

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b = ab^2, for a,b in Q Find which of the binary operations are commutative and which are associative.

Consider the binary operations * : R xx R to R and o: R xx R to R defined as a * b = |a-b| and a o b = a for all a,b in R . Show that '*' is commutative but not associative, 'o' is associative but not commutative.

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b = a^2 + b^2, for a , b in Q Find which of the binary operations are commutative and which are associative.

Let * be a binary operation defined on Q, the set of rational numbers, as follows: a*b = (a-b)^2, for a,b,inQ Find which of the binary operations are commutative and which are associative.